Cosmological singularities in non-standard backgrounds

The universe's late-time acceleration has prompted a great deal of research into cosmological singularities. Recent work has seen a proper classification of such singularities into strong and weak based on their strength, with weak singularities including the sudden, w, and big freeze singularities and strong singularities including the big rip singularity. So I'd be discussing a variety of new findings in this regard in various exotic cosmologies in this talk. To begin, we consider RS-II Braneworld-based scalar field dark energy models and demonstrate the presence of finite time singularities in these regimes from a dynamical system perspective, using the Goriely-Hyde singularity analysis method. This approach is general in the sense that it is not restricted to any specific class of potentials or any constrained parameter region for the brane tension, and it is valid for both Quintessence and Phantom dark energy regimes. We show that finite time singularities can exist in these models for a limited set of initial conditions, and that this result holds regardless of whether the swampland dS conjecture is taken into account, and we also classify the physical nature of these singularities. I then discuss about the occurence of type V singularities in non- GR based cosmological backgrounds, namely ones of the RS-II, f(R) and Chern-Simons type and show that type V singularities occur in almost the same conditions in all these scenarios as they do in the usual GR based cosmology. However, I then discuss that if we consider inhomogenous equations of state for matter than the occurence conditions of these singularities changes considerably ( for f(R) gravity, these could be totally removed too). Finally, we discuss singularities in an asymptotically safe cosmology where I show that one can have Type I - Type IV singularities in such a cosmology for various versions of the equation of state and that the singularities can occur both in finite and infinite time. The conditions in which these singularities occur is significantly different than how they occur in the standard cosmology, with the formulations being even more involved.